Finite Group Databasebeta

← #11870504

Subgroups — #11870504

Order 1152.

1109 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 1109 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic, complemented
3C3×#5218C212yesmaximal
4#10591497C212yesmaximal, complemented
5#10591495C212yesmaximal, complemented
6#10591445C214yesmaximal, complemented
7#10591126C212yesmaximal, complemented
8#10591061C211yesmaximal, characteristic, complemented
9#80132—32nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C2×#3757—21no—
13D4×C3⋊Dic3—21no—
14D4×C3⋊Dic3—21no—
15D4×C3⋊Dic3C2212yes—
16D4×C3⋊Dic3C2212yes—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#214C2214yes—
20C3×#924C2212yes—
21#63982—21no—
22#63957—21no—
23#63919C2211yescharacteristic, complemented
24#63873C2211yescharacteristic, complemented
25#63870—21no—
26#63843C2212yescomplemented
27#63838—21no—
28C3×#832C2214yes—
29C3×#830C2212yes—
30#63573C2214yescomplemented
31#63572C2212yescomplemented
32#63566C2214yescomplemented
33#63553C2212yescomplemented
34C2×D4×Dic3—32no—
35C2×D4×Dic3—61no—
36#5622—32no—
37C3×#450—32no—
38#5218D312yes—
39#5162—34no—
40Dic3×SD16—34no—
41#5043—32no—
42#4761—34no—
43#4758—34no—
44#4721—32no—
45#4718—32no—
46C24×C32—21no—
47C2×C32×D4—24no—
48C2×C32×D4—21no—
49C2×C32×D4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—44no—
55C22×C3⋊Dic3D411yescharacteristic
56C22×C3⋊Dic3D411yescharacteristic
57C2×C3×Dic6C2312yes—
58C2×#627—21no—
59#3757—22no—
60#3757—22no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)C2312yes—
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C3×#217—22no—
68C3×#214—28no—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—22no—
71C2×C3×C3⋊C8C2314yes—
72#3724—21no—
73#3724—21no—
74#3724—21no—
75Dic3⋊Dic3—22no—
76Dic32—22no—
77#3101—91noSylow
78C22×C3×D4—21no—
79C22×C3×D4C2×D312yes—
80C23×Dic3—62no—
81C23×Dic3—62no—
82C2×C3×SD16—34no—
83C3×C22⋊Q8—32no—
84C2×#217—62no—
85C2×#217—62no—
86Q8×Dic3—32no—
87#944—32no—
88D4×Dic3—34no—
89D4×Dic3—34no—
90D4×Dic3—62no—
91D4×Dic3—62no—
92D4×Dic3—62no—
93D4×Dic3—62no—
94D4×Dic3—62no—
95D4×Dic3—62no—
96C2×#214C2×D314yes—
97C2×C4⋊Dic3—32no—
98C2×C4⋊Dic3—61no—
99#924C2×D312yes—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—61no—
102#889—62no—
103#888—32no—
104#887—32no—
105#887—62no—
106#878—62no—
107#877—62no—
108C3×#102—34no—
109C3×C22⋊C8—32no—
110#835—34no—
111#832C2×D314yes—
112#830C2×D312yes—
113#817—34no—
114#816—34no—
115Dic3⋊C8—34no—
116C8×Dic3—34no—
117#808—34no—
118C23×C32—24no—
119C23×C32—22no—
120C23×C32—42no—
121C23×C32—42no—
122C23×C32C2×D411yescharacteristic
123C32×D4—24no—
124C32×D4—22no—
125C32×D4#4114yes—
126C2×C32×C4—22no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2411yescharacteristic
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—42no—
132C2×C3⋊Dic3—44no—
133C2×C3⋊Dic3—44no—
134C2×C3⋊Dic3SD1614yescomplemented
135C2×C3⋊Dic3C2×D411yescharacteristic
136C2×C3⋊Dic3C2×D411yescharacteristic
137C2×C3⋊Dic3C2×D411yescharacteristic
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C3×Dic6—24no—
142#627—42no—
143C3×C3⋊C8—24no—
144#533—91no—
145C2×C4×D4—91no—
146#483—92no—
147#476—92no—
148#461—92no—
149#450—32no—
150C4×SD16—94no—
151#431—91no—
152C24×C3—22no—
153C24×C3—22no—
154C2×C3×Q8—32no—
155C2×C3×D4—22no—
156C2×C3×D4—28no—
157C2×C3×D4—28no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4C22×D314yes—
161C22×C3×C4—21no—
162C22×C3×C4C22×D312yes—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—64no—
168C22×Dic3—64no—
169C22×Dic3—62no—
170C22×Dic3—64no—
171C22×Dic3—64no—
172C22×Dic3—62no—
173C22×Dic3—128no—
174C22×Dic3—128no—
175C2×Dic6—62no—
176C2×Dic6C22×D312yes—
177C3×SD16—68no—
178C2×C3×C8—34no—
179C3×C4⋊C4—32no—
180C3×C4⋊C4—62no—
181C3×C22⋊C4—62no—
182#217—22no—
183#217—64no—
184#217—64no—
185#217—64no—
186#217—64no—
187#214—28no—
188C4⋊Dic3—34no—
189C4⋊Dic3—62no—
190C4⋊Dic3—62no—
191C4⋊Dic3—62no—
192C4⋊Dic3—62no—
193C4⋊Dic3C22×D312yes—
194Dic3⋊C4—22no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—62no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—32no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—62no—
208C4×Dic3—62no—
209C2×C3⋊C8C22×D314yes—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—24no—
213C22×C32—48no—
214C22×C32—42no—
215C22×C32—42no—
216C22×C32C2×SD1612yes—
217C22×C32C22×D411yescharacteristic
218C32×C4—21no—
219C32×C4C2×#4112yes—
220C3⋊Dic3—21no—
221C3⋊Dic3—21no—
222C3⋊Dic3—42no—
223C3⋊Dic3C2×SD1612yes—
224C3⋊Dic3C2×SD1612yes—
225C3×Dic3—42no—
226C3×Dic3—42no—
227C22×D4D3211yescharacteristic
228C23×C4—181no—
229C2×SD16—34no—
230C4⋊Q8—91no—
231C4⋊Q8—91no—
232#125—181no—
233C22⋊Q8—32no—
234C22⋊Q8—181no—
235C4×Q8—92no—
236C4×Q8—181no—
237C4×D4—92no—
238C4×D4—92no—
239C4×D4—181no—
240C4×D4—181no—
241#117—181no—
242C2×C4⋊C4—91no—
243C2×C22⋊C4—181no—
244C2×C42—91no—
245#106—94no—
246C4⋊C8—92no—
247#103—94no—
248#102—34no—
249C22⋊C8—32no—
250C4×C8—92no—
251C23×C3—24no—
252C23×C3—28no—
253C23×C3—28no—
254C23×C3—24no—
255C23×C3—21no—
256C23×C3—44no—
257C23×C3—44no—
258C23×C3—44no—
259C23×C3—44no—
260C23×C3D3×D412yes—
261C3×Q8—64no—
262C3×D4—28no—
263C3×D4—28no—
264C3×D4—24no—
265C3×D4—24no—
266C3×D4—24no—
267C3×D4#23718yes—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4D3×D412yes—
275C2×C3×C4C23×D312yes—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—38no—
279C2×Dic3—32no—
280C2×Dic3—32no—
281C2×Dic3—32no—
282C2×Dic3—32no—
283C2×Dic3—64no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—128no—
291C2×Dic3—128no—
292C2×Dic3—122no—
293C2×Dic3—128no—
294C2×Dic3—128no—
295C2×Dic3—122no—
296C2×Dic3—124no—
297C2×Dic3—124no—
298Dic6—24no—
299Dic6—124no—
300C3×C8—64no—
301C3⋊C8—24no—
302C2×C32—22no—
303C2×C32—44no—
304C2×C32#52511yescharacteristic
305C2×C32C22×SD1611yescharacteristic
306C2×C32#57511yescharacteristic
307C24—21no—
308C2×Q8—32no—
309C2×Q8—181no—
310C2×D4—24no—
311C2×D4—21no—
312C2×D4C2×D3212yes—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—182no—
316C22×C4—182no—
317C22×C4—181no—
318C22×C4—364no—
319C22×C4C2×D3211yescharacteristic
320SD16—68no—
321C2×C8—34no—
322C4⋊C4—32no—
323C4⋊C4—62no—
324C4⋊C4—92no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—182no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C22⋊C4—62no—
331C22⋊C4—182no—
332C22⋊C4—182no—
333C42—91no—
334C42—91no—
335C42—91no—
336C42—91no—
337C42—182no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—28no—
343C22×C3—28no—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—44no—
347C22×C3—416no—
348C22×C3—416no—
349C22×C3—44no—
350C22×C3—44no—
351C22×C3—44no—
352C22×C3D3×SD1614yes—
353C22×C3C2×D3×D412yes—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—122no—
358C3×C4—122no—
359C3×C4C2×#23714yes—
360Dic3—34no—
361Dic3—34no—
362Dic3—42no—
363Dic3—42no—
364Dic3—62no—
365Dic3—62no—
366Dic3—62no—
367Dic3—62no—
368Dic3—121no—
369Dic3—121no—
370Dic3—124no—
371Dic3—124no—
372C32#310111yescharacteristic, complemented, Sylow
373C23—24no—
374C23—22no—
375C23—42no—
376C23—42no—
377C23#381111yescharacteristic
378Q8—64no—
379Q8—362no—
380D4—24no—
381D4—22no—
382D4#380514yes—
383C2×C4—22no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—94no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—182no—
392C2×C4—364no—
393C2×C4—364no—
394C2×C4—361no—
395C2×C4—362no—
396C2×C4#381111yescharacteristic
397C2×C4C22×D3211yescharacteristic
398C8—64no—
399C2×C3—24no—
400C2×C3—24no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—48no—
405C2×C3—48no—
406C2×C3#558612yes—
407C2×C3C2×D3×SD1612yes—
408C2×C3#577312yes—
409C22—21no—
410C22—21no—
411C22—24no—
412C22—48no—
413C22—42no—
414C22—42no—
415C22#6393012yes—
416C22C2×#381111yescharacteristic
417C4—21no—
418C4—92no—
419C4—92no—
420C4—122no—
421C4—122no—
422C4—181no—
423C4—181no—
424C4—362no—
425C4C2×#380512yes—
426C3—21no—
427C3#8013212yescomplemented
428C2—22no—
429C2—44no—
430C2#1059510111yescharacteristic
431C2C2×#6393011yescharacteristic
432C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10594810C2semidirect
4. #10591497C2semidirect
5. #10591495C2semidirect
6. #10591445C2semidirect
7. #10591126C2semidirect
8. #10591061C2semidirect
23. #63919C22semidirect
24. #63873C22semidirect
26. #63843C22semidirect
30. #63573C22semidirect
31. #63572C22semidirect
32. #63566C22semidirect
33. #63553C22semidirect
134. C2×C3⋊Dic3SD16semidirect
372. C32#3101semidirect
427. C3#80132semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D4×C3⋊Dic32
#105948102
C3×#52182
#105914972
#105914952
#105914452
#105911262
#105910612
#801323